用标准正态分布求函数积分,
问题描述：
用标准正态分布求函数积分,
答
答
t = x/2^(1/2), t^2 = x^2/2,
dt = dx/2^(1/2),
t: -无穷-〉正无穷， x: -无穷-〉正无穷
S_{ t:-无穷-〉正无穷}e^(-t^2)dt =
= S_{x:-无穷-〉正无穷}2^(-1/2)e^(-x^2/2)dx =
= (PI)^(1/2)S_{ x:-无穷-〉正无穷}(2PI)^(-1/2)e^(-x^2/x)dx =
= (PI)^(1/2)*1
= (PI)^(1/2).
PI = 3.1415926
答